In many change point problems it is reasonable to assume that compared to a
benchmark at a given time point $t_0$ the properties of the observed stochastic
process change gradually over time for $t >t_0$. Often, these gradual changes
are not of interest as long as they are small (nonrelevant), but one is
interested in the question if the deviations are practically significant in the
sense that the deviation of the process compared to the time $t_0$ (measured by
an appropriate metric) exceeds a given threshold, which is of practical
significance (relevant change).
In this paper we develop novel and powerful change point analysis for
detecting such deviations in a sequence of gradually varying means, which is
compared with the average mean from a previous time period. Current approaches
to this problem suffer from low power, rely on the selection of smoothing
parameters and require a rather regular (smooth) development for the means. We
develop a multiscale procedure that alleviates all these issues, validate it
theoretically and demonstrate its good finite sample performance on both
synthetic and real data.

Este artículo explora los viajes en el tiempo y sus implicaciones.

Descargar PDF: